Category: Teaching Elementary Math

Geometry Math Stars for Christmas!

Learn and Practice Geometry by Making Your own Family Christmas Tree Star Ornaments!  Great for decorating your Christmas Tree or for making a Gift to give to a friend or family member.

Materials Needed:

Colored Markers or Crayons

Glue or Scotch Tape


Colored Yarn or String


Colorful Recycled Paper (tissue boxes, flyers, old wrapping, etc.)

Directions for Christmas Star Cutout:

1.Cut out the outline.

2.Cut along all heavy lines.

3.Score plain lines on the front.

4.Score dotted lines on the back.

5.Fold triangles upword along plain lines.

6.Fold triangles downword along dotted lines.

7.Glue or tape tabs to form small tetrahedrons.

8.Continue until you have your Geometry Christmas Star Tetrahedron.

Everyone has their own Star!  Everyone has their own Inner Light!  With Favorite colors, draw your stars, or print this page and cut the pattern of the star out.

Inside each shape on the side of the star, write your name and birthday.  Or – write the names of each member of your family (If you Wish, your family / family Tree Star can be made of relatives (close or extended), friends and/or adopted family – as long as you write each name on each.  You could make many stars – a pretty star for each member of your Christmas Tree, or write everyone’s name on the same Star.

Color and Decorate each one with colored markers, crayons, sparkles, gluing pieces of recycled Christmas paper from last year.  You can also write happy words all over your star like Love, Divine Wisdom, Infinity, Pure Spirit, Fun and Harmony!

Remember to Decorate your Stars!

Glue Yarn / Strong at the top  into a 2 inch loop and tie a knot at the end

Hang your Christmas Geometry Math Stars and Decorate your Tree at Home or in your Classroom!

Have a Merry Christmas and Happy Holiday!

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Reference for Star Tetrahedron Geometry Template: “The Ancient Secret of the Flower of Life,” Vol. 2, by Drunvalo Melchizedek

Drawing with Pythagoras

“Pythagorean Theorem?!!”…I know what you are thinking…..(You can say to your class)…..”OMG  Teacher…..What could we possibly ever use this for, in the future of our lives?“……Well, in this article, we talk about real life examples of using the Pythagorean Theorem.  First let’s learn a basic calculation, corresponding to the diagram here to the <<left, followed by a bit of Pythagorean history.  The basis of the theorem is that the Area of the 2 Squares of the 2 Lines that form the Right Angle of a Right Triangle are the equivalent ( = ) Area of the Square that opposes them in the Triangle. If you look at the diagram here to the << left, the Areas of “a” added to “b” = the Area of “c” (the Square of the opposite line (or “leg”). That opposite line (or  “c” “leg”) is called the hypotenuse. Also, if one of the lines “a” of the right triangle is 4 inches and the other line “b”  is 6 inches, we can calculate how long the hypotenuse is, or the “third leg”. Letting a = 4, b=6, and c= the length of the hypotenuse.  (4)^2 + (6)^2 = c^2. Accordingly, 4 x 4 =16, and 6 x 6 = 36. Thus, 16 + 36 = 52. The square root of 52 is approximately 7.21 , hence the length of the hypotenuse or “third leg“ of the right triangle, is 7.21 inches.

The Pythagorean Theorem is named after the Greek mathematician Pythagoras. Many believe the first discovery and proving of this ancient math theorem came before Pythagoras, but since no tangible account of this has yet been documented, it is named as such. If that was true, however, we wonder what another name of the theorem would have been, and from what country and nation? (a fun question to ponder).  The Pythagorean Theorem can be used with any shape and for any formula that squares a number. And, in fact, the area of any shape can be computed from any line segment squared.  (reference also for Diagram Above).   Apparently, even the teenage Brainiac Lisa Simpson from The Simpsons television series knows all about Pythagoras.  On this site, there are some cool diagrams showing the differences of Lines (Segments / Legs), Radius, and Area:  And, to assist in figuring out these math scenarios, this site offers tabs for entering in numbers to calculate the square root of the numbers in question:

Finally, here are a few Real Life Examples:

Meet Me at The Corner:
Let’s say Stephanie and Maria are meeting at the Hiking Trail Entrance on the corner of Saanich Rd. and Cedar Rd. One phones the other on her mobile phone and asks, “How long will it be before you arrive at the entrance?”… “Well, let’s estimate by first finding out how far away we are from each other.” In present time, Stephanie is on Saanich Rd. to and is 10 miles away. Meanwhile, Maria is on Cedar Rd. and is 4 miles away.  How far away from one another are Stephanie and Maria?  The distance between them = a^2 + b^2 = c^2 or, respectively: 10^2 (10 squared) + 4^2 (4 squared); or respectively, 100 +16 = 116 miles. The square root of 116 is 10.77. Thus, Stephanie and Maria are 10.77, almost 11 miles away from one another. Hence, they figure they will be another hour on their bicycles to meet one another to go hiking.

Firefighters Needing to Know Height of a Building:
3 Firefighters receive a call to help Ann rescue her cat Tia from the Oak Tree outside her window. The tree is about 3 stories tall, and the Tia, after chasing a squirrel, is stuck on a branch at about the height of 2 stories of her house. The height to the branch may be 20 feet, and the firefighters have to put the ladder about 10 feet away from the Oak Tree in order to go around Ann‘s shed. How long of a ladder do the firefighters need in order to rescue Ann‘s cat? a^2 + b^2 = c^2 or, respectively: (20)^2 + (10)^2 = 2^2, the length of ladder required. 400 + 100 = 500. The square root of 500 is approximately 22.37. The firefighters extend their expandable ladder to be approximately 23 feet, whereas they need at least 22.37 feet to safely reach the Oak branch. Ann’s cat Tia is rescued and All are Happy!

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Teaching Math: A Breeze when Incorporating Favorite Interests

Teaching math in the Elementary classroom can be a challenge, as all elementary math teachers know, but when favorite activities of students are incorporated into the curriculum, it can be a breeze. When students have a required learning skill to attain, and they incorporate their favorite interests, then there is inspiration – and the student becomes “self-motivated”.    This is a great First Item to address with the rounds of new students returning for the fall season.  Find out Learners’ Favorites, and keep the list in a special file.

Then, as the year progresses, if a student is having a challenge learning a particular new math lesson, Teachers can refer to the student’s personal file of “Favorites Activities List”.  At this time, then, introducing the association and how that interest relates to the new lesson.

Example No. 1:  Young Matthew enjoys playing or watching the game of baseball. That is included in their list of favorite activities.  November rolls around, and the lesson of drawing shapes in geometry arises, but Matthew is not grasping the concepts.  If looking down onto a Baseball Diamond from an aerial perspective, the shape of Square is easily seen in the formation of the 4 bases on the ball field.  As well, the shape of the bases individually, is a square.

Then show in sequence what happens when the player runs to first base, second, third and fourth, demonstrating the making of a Straight Line 4 times, and in consecutive order. Within each corner, while the player stands on the base, the player looks down at both straight lines that connect, and the player can then see a perfect Right Angle of 90 degrees.  Drawing a line across from the base to the left to the base t the right demonstrates a perfect Right Triangle.

Suddenly a light is switched on in the child’s brain, and Matthew is on the way to understanding the concept of geometry.  Not only do they understand it on paper in 2-D form, but now in 3-D form, in the context of a baseball game, in a real life scenario.

Example No. 2:
  Ashley likes archery.  Archery is included in her favorite activities list.  While imaging and practicing her archery skills, she sees concentric circles – one inside the other.  When a line is drawn from her bow to the target, she demonstrates a perfect straight line.  Hence, she has a different yet equally effective association of a favorite interest to relate to the concepts in geometry –  as Mathew’s love of baseball.  Imagine now that Susie, not only is attaining the required skills the in geometry lesson, but is also having fun while doing it, and has developed self-motivation and interest in learning math.

In these examples, both sides of the Brain are exercised, (Left Right Brain Learning and Thinking) new neural connectors and dendrites grow, and you have encouraged the growth of a healthy developing young brain.

Start the school year off right, and find out what your students’ favorite activities are. Keep the lists on file, and refer to them from time to time during the school year.  You may be surprised at the effectiveness of this subtle teaching tool.

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Flower Geometry on Summer Vacation

Summer can be fun Learning Math on your camping trip or at home in your backyard.  An interesting approach to learning geometry in elementary math is by the study of flowers found in your backyard (or schoolyard in Spring or Fall).  Have your class walk around the local grounds, or give them an assignment to go home and document in their notebooks, different flowers, counting the number of petals in the flowers.

A second item, if time permits is to have the Learners identify the flowers as well.  Upon arrival back in the classroom, Learners identify, with their geometry charts, which geometric pattern or shape the flower has grown into.



Eyes  (peepers for finding flowers)

Camera, if available


Pencil and Good Eraser

Pencil Crayons in various colors


Compass (if you wish to measure angles in the shapes)



Next, Learners draw in their notebooks the geometric shape the flower is equated with, and beside the shape, a simple drawing of the flower, coloring the flower drawing with the corresponding color of the petals.  If possible, 3-D forms can be cut out and interlocked together, with a string glued into the top of the start and made into Christmas ornaments.


Yellow Blue-eyed Grass:  (photo Above) 6-Petaled Yellow Wild Flower (that also grows in Bluish Purple and White); found in tall grasses who / that opens up only with the sun, and closes at the end of the day when the sun sets, or on cloudy days.

Geometric pattern:  6-pointed Star Tetrahedron; Two 3-Dimensional Interlocking Equilateral Triangles with a conjoining dot in the middle.  These 2 photos show the star tetrahedron (6-pointed) both in 2-dimensional form (as it would be if drawn flat on a piece of paper).  The second photo is a rendition of a 3-dimensional form (as if it were hanging as an ornament in a tree).   SourceURL:file:///Users/sheila/Desktop/Summer%20Flower%20Geometry.doc

When looking, aim for the pattern that is found when counting the Number of Petals in the Flowers.  In the Yellow Blue-Eyed Grass, there are 6 petals which if gazed at in a 3-Dimensional way, one can see the pattern of the 6-pointed star tetrahedron.

This can be a fun activity to do while on summer vacation – or during the schoolyear in Spring and Fall, and depending what climate area your school is, it can be done during winter as well.

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The Fibonacci Sequence

Fibonacci is a Number / Integer Sequence, that when applied in geometrical form, manifests in a Spiral as in that of a Pine Cone or a SeaShell.  The sequence was named after an Italian mathematician known as Leonardo of Pisa (or Leonardo de Fibonacci).  In 1202, he wrote a book called Liber Abaci in which he gives name to the number sequence.  There are historical examples of the sequence showing up in East Indian mathematics as well.

Add two consecutive numbers from the sequence to equal the next one following.  The basic sequence looks like this:

0,         1,            1,            2,            3,            5,            8,            13,            21,            34,            55,            89,            144,            233,            377, etc., etc.

That is:



2+1 (the “number” before)=3

3+2 (the number before)=5








etc., etc., etc.

In Spiritual Theory, Life must look back on itself before it can move forward.  In Relation to the human species, we must look back toward our Ancestors to learn Wisdom and give Gratitude to Life in the Present in order to move into the Future in the best way and in the Best Direction.  Because in theory the Spiral is not quantifiable in the concrete sense; i.e. it is a sequence that is Infinite (no final end number), mathematicians use straight lines around the spirals to give it as close to a concrete geometric equation as is possible.  Hence, the spiral looks like a spiral of expanding squares as shown here, and is known as the Golden Mean Ratio.  In biological settings, The Fibonacci Sequence can be seen in the Spirals of the Pinecone, in the Branch growth pattern of trees, the mini-fruit pieces of the Pineapple, the Artichoke flower, a Fern during its uncurling, and Seashells.  The sequence can also be seen in Rabbit breeding patterns, and the family tree of Honeybees.

In relation to Rabbits, Fibbonaci posed this question during the middle ages:

Rabbits can mate at the age of one month, a pretty fast breeding cycle for an animal. If a rabbit population was ideal (though not biologically realistic), if one assumed that a new pair of rabbits (one male and one female) were in a field, and after the end of one month, that pair had another pair, and every pair had another pair, how many pairs would there be after one year?

End of First Month:  1 New Pair

End of Second Month:  2 New Pairs

End of Third Month: The Original Female makes a Second Pair, Equaling 3 Pairs in the field

End of The Fourth Month:  First Female makes a Third Pair, The Female born in the Second Month makes Her First Pair, etc., Now Equaling 5 Pairs.

End of “n”th Month, Number of Pairs = The Number of New Pairs (= Number of Pairs in Month “n” – 2 + Number of Pairs alive in Previous Month “n” -1.

This is the “n”th Fibonacci Number, and it looks like this:

There are numerous other examples in nature shown in this site, as well as in class activities you can do to demonstrate the Fibonacci.

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Secret Chocolate Fraction Codes

It is Post-Halloween and we are not quite finished making chocolate FUN just yet!  Here is a fun and easy fractions game to organize that is low-cost and easily teachable, any time of the year.


  • Crayola Markers, 3 for each student
  • One Organic Chocolate Bar for each student
  • Piece of Paper

Have everyone bring in a Whole Chocolate Bar (organic if possible – it is healthier!)  –  One that has an equal number of squares in it.  They do not all have to be the same number of squares, but if they are, it is a bit easier for instructions.

Using a non-toxic marker (Crayola is my favorite), have each Learner draw a gridline across the paper on the outside of the bar in their favorite color.,BASICS

Step 1:  Counting 1-12 (usually,  this is the number of squares in a bar.)  If it is different, then  ask the learner to count, respectively re their bar, and write down on paper the basic 12 fractions of their bar:

1/12, 2/12, 3/12, 4/12, 5/12, 6/12, 7/12, 8/12, 9/12, 10/12, 11/12, 12/12

Step 2: Then secretly and individually, each student colors a different amount of squares in each bar, using 3 different colored markers.  Encourage Sharing/Trading markers if there is not enough markers to go around.

Step 3: Then, everyone divides into pairs, and one at a time – without  showing each other what they have colored – each student  guesses what 3 numbered fractions the other one has colored.

Eg/  Susan colored 3 squares in Red, 2 squares in Yellow, and 7 squares in Purple.  Therefore, Susan’s Secret Fraction Codes are:

3/12, 2/12 and 7/12.

Bob colored 3 squares in Blue, 6 squares in Green, and 3 Squares in Orange. Therefore, Bob’s Secret Fraction Codes are:

3/12, 6/12 and 3/12.

Step 4:  After successfully guessing the other’s Secret Fractions, each one guesses the 3 respective Colors – of each Fraction Code.

Step 5: Once they have successfully guessed the other one’s Secret Fraction Codes, have them, TOGETHER then, add all 3 to make the Whole Number One 1.

Eg/ Susan’s Secret Fraction Codes look like this:

3/12 + 2/12 + 7/12 = 12/12 = 1

Bob’s Secret Fraction Codes look like this:

3/12 + 6/12 + 3/12 = 12/12 = 1

Last Step:  Everyone share their Chocolate Bars with The Teacher! lolololololol

Enjoy!  Yum.

Love The Earth!

Remember to Recycle both the paper and the tinfoil or plastic that the bar was wrapped in!  The more Recycling and Care for The Earth, the more Pretty Colored Feathers (or Stars)you receive from The Teacher!

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Gratitude for Teachers: Goals of Teaching Elementary Math

Giving teachers a heads up Thank You is something that happens usually once or twice a year – maybe Valentine’s Day, Christmas time…we often wonder if parents and kids truly realize the giving that teachers do in their daily classroom lives – so we want to say Thank You!

Making the task of teaching elementary math a little easier on the shoulders of the teachers, here is a checklist of goals for the year, to check off through the year, and give yourself a pat on the back for all of your teaching efforts and successes.  Given all that teachers do in the run of a teaching day, month, term and year, saying thank you is the least any of us can do.

Heart Math

What colors of candy are more popular in a typical bag of Valentine Hearts?  World over, kids pretty much enjoy receiving and giving Valentines to their friends on Valentine’s Day.  This year, make it a math learning experience, so the fun is included in the work.

Here is a Fun Idea for making it a Happy Heart Math day applicable to Grades 1-4 that encourage comprehension skills of:

Assessing, making predictions, and organizing

Counting, creating, adding, comparing

Listing/ recording data, and reading a graph

This activity is about making heart graphs, inspiring practice and comprehension for making graphs in general, and using fun hearts specifically.


Bag of Multi-colored Candy Hearts, about 5/6 cups (1 cup worth for each 5 students)

Financial Literacy at home, in School and Society

Earning, saving, spending, investing, budgeting, collecting, and giving are all part of handling money.  And handling money wisely is what financial literacy at home, school and in society is all about.

Modern governments want to develop financial literacy among consumers in society. This means improving the ability to understand money matters, applying that knowledge and developing responsibility for making money decisions at the grade school level.  Money literacy is an important life skill. Although it has minimally been taught in school in courses such as

Real-World Activities for Teaching Fractions

For many elementary age children, fractions seem like a foreign language that they likely may never use in real life.  To challenge this thinking, we can use real-world activities that illustrate just how fractions help their parents, and how they will help them as they grow up.

  • Teach them to use the ruler. Rulers are really handy for teaching real-world applications for fractions.  Most of them are already divided into halves, fourths, eighths, even sixteenths.  It’s easy to show them that two halves are the same as one. . . that two fourths are the same as one half, and four fourths are the same as one, and so on.
  • Teach them to use measuring cups and spoons.  Bring lots of these dishes to class and give one measuring spoon and cup to each child.  Ask them to pour one cup of water into a tall glass. Now take guesses from the students:  How many half cups do they think it takes to fill a cup? How many quarter cups will it take?  How